MathPlotAI Logo MathPlotAI

Reflecting about Planes: AR Template

Reflecting about Planes: AR Template
Loading the math board and drawing, please wait…
2020-09-30 00:16
Solid GeometryTransformationGeometric Construction
In collections Transformations! (Geometry)
This example demonstrates dynamic effects of plane reflection and geometric transformations. Key mathematical concepts include reflection, similar triangles, vectors, and geometric construction. Construction involves GeoGebra commands like Plane, Mirror, Segment, Intersect, etc. Suitable for middle or high school math teaching to understand plane geometry transformations and spatial geometry relationships.

GeoGebra Commands & Parameters

  1. Plane(B, C, A) → a
  2. Pyramid(E, D, F, G) → b, faceDEF, edgeFG, faceDEG, faceDFG, faceEFG, edgeDE, edgeDF, edgeEF, edgeEG, edgeDG
  3. Mirror(b, a) → b'
  4. Mirror(D, a) → D'
  5. Mirror(E, a) → E'
  6. Mirror(G, a) → G'
  7. Mirror(E, a) → E'_1
  8. Mirror(D, a) → D'_1
  9. Segment(E'_1, D'_1) → edgeDE'
  10. Mirror(D, a) → D'_2
  11. Mirror(F, a) → F'
  12. Segment(D'_2, F') → edgeDF'
  13. Mirror(D, a) → D'_3
  14. Mirror(G, a) → G'_1
  15. Segment(D'_3, G'_1) → edgeDG'
  16. Mirror(F, a) → F'_1
  17. Mirror(E, a) → E'_2
  18. Segment(F'_1, E'_2) → edgeEF'
  19. Mirror(G, a) → G'_2
  20. Mirror(E, a) → E'_3
  21. Segment(G'_2, E'_3) → edgeEG'
  22. Mirror(F, a) → F'_2
  23. Mirror(G, a) → G'_3
  24. Segment(F'_2, G'_3) → edgeFG'
  25. Line(F, F'_2) → f
  26. Line(G, G'_2) → g
  27. Line(D, D') → h
  28. Line(E, E') → i
  29. Intersect(f, a) → H
  30. Angle(F, H, B) → α
  31. Dilate(F, If[0 < SlideMe ≤ 1, 1 - SlideMe, 0], H) → F'_3
  32. Segment(F, F'_3) → j
  33. Dilate(H, If[1 < SlideMe ≤ 2, 2 - SlideMe, 0], F'_2) → H'
  34. Segment(H, H') → k
  35. Plane(H, C, F'_2) → l
  36. Rotate(F, If[2 < SlideMe ≤ 3, ((SlideMe - 2) * π), π], H, l) → F'_4
  37. Rotate(F'_3, If[2 < SlideMe ≤ 3, ((SlideMe - 2) * π), π], H, l) → L
  38. Segment(F'_4, L) → j'
  39. Dilate(B, If[0 < SlideMe ≤ 1, 1 - SlideMe, 0], H) → B'
  40. Segment(B, B') → m
  41. Line((0, 0, 0), (1, 0)) → p
  42. Line((0, 0, 0), (0, 1, 0)) → q
  43. Line((0, 0, 0), (0, 0, 1)) → r

AI Drawing Prompt Reference

Create a 3D geometry teaching illustration featuring a reflection plane defined by three points and a quadrilateral pyramid with its mirror image across that plane. Show the original pyramid and its reflected version with all corresponding edges clearly visible to demonstrate symmetry. Include line segments connecting each vertex of the original pyramid to its mirror image. Add slider-controlled animations showing three phases: contraction, translation, and rotation to illustrate geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.